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We prove the existence on long time scales of the solutions to the Cauchy problem for a version of weakly transverse Boussinesq systems arising in the modeling of surface water waves. This system is much more complicated than the isotropic Boussinesq systems because dispersion is only present in the x-direction, leading to anisotropic eigenvalues in the linearized system. This anisotropic character leads to loss of y-derivatives for the solutions. To overcome this main difficulty our strategy is to symmetrize the system by introducing suitable good unknowns in the sense of [3]., Comment: 45 pages

Bell non-locality is closely related with device independent quantum randomness. In this paper, we present a kind of sum-of-squares (SOS) decomposition for general Bell inequalities in two qubits systems. By using the obtained SOS decomposition, we can then find the measurement operators associated with the maximal violation of considered Bell inequality. We also practice the SOS decomposition method by considering the (generalized) Clauser-Horne-Shimony-Holt (CHSH) Bell inequality, the Elegant Bell inequality, the Gisin inequality and the Chained Bell inequality as examples. The corresponding SOS decompositions and the measurement operators that cause the maximum violation values of these Bell inequalities are derived, which are consistent with previous results. We further discuss the device independent quantum randomness by using the SOS decompositions of Bell inequalities. We take the generalized CHSH inequality with the maximally entangled state and the Werner state that attaining the maximal violations as examples. Exact value or lower bound on the maximal guessing probability using the SOS decomposition are obtained. For Werner state, the lower bound can supply a much precise estimation of quantum randomness when $p$ tends to $1$., Comment: 10 pages, 2 figures

The strategic orchestration of football matchplays profoundly influences game outcomes, motivating a surge in research aimed at uncovering tactical nuances through social network analysis. In this paper, we delve into the microscopic intricacies of cooperative player interactions by focusing on triadic motifs within passing networks. Employing a dataset compiled from 3,199 matches across 18 premier football competitions, we identify successful passing activities and construct passing networks for both home and away teams. Our findings highlight a pronounced disparity in passing efficiency, with home teams demonstrating superior performance relative to away teams. Through the identification and analysis of 3-motifs, we find that the motifs with more bidirectional links are more significant. It reveals that footballers exhibit a strong tendency towards backward passes rather than direct forward attacks. Comparing the results of games, we find that some motifs are related to the goal difference. It indicates that direct and effective forward passing significantly amplifies a team's offensive capabilities, whereas an abundance of passbacks portends an elevated risk of offensive futility. These revelations affirm the efficacy of network motif analysis as a potent analytical tool for unveiling the foundational components of passing dynamics among footballers and for decoding the complex tactical behaviors and interaction modalities that underpin team performance.

We introduce Diff-Tracker, a novel approach for the challenging unsupervised visual tracking task leveraging the pre-trained text-to-image diffusion model. Our main idea is to leverage the rich knowledge encapsulated within the pre-trained diffusion model, such as the understanding of image semantics and structural information, to address unsupervised visual tracking. To this end, we design an initial prompt learner to enable the diffusion model to recognize the tracking target by learning a prompt representing the target. Furthermore, to facilitate dynamic adaptation of the prompt to the target's movements, we propose an online prompt updater. Extensive experiments on five benchmark datasets demonstrate the effectiveness of our proposed method, which also achieves state-of-the-art performance., Comment: ECCV 2024

Cell image segmentation is usually implemented using fully supervised deep learning methods, which heavily rely on extensive annotated training data. Yet, due to the complexity of cell morphology and the requirement for specialized knowledge, pixel-level annotation of cell images has become a highly labor-intensive task. To address the above problems, we propose an active learning framework for cell segmentation using bounding box annotations, which greatly reduces the data annotation cost of cell segmentation algorithms. First, we generate a box-supervised learning method (denoted as YOLO-SAM) by combining the YOLOv8 detector with the Segment Anything Model (SAM), which effectively reduces the complexity of data annotation. Furthermore, it is integrated into an active learning framework that employs the MC DropBlock method to train the segmentation model with fewer box-annotated samples. Extensive experiments demonstrate that our model saves more than ninety percent of data annotation time compared to mask-supervised deep learning methods.

Multiple complex degradations are coupled in low-quality video faces in the real world. Therefore, blind video face restoration is a highly challenging ill-posed problem, requiring not only hallucinating high-fidelity details but also enhancing temporal coherence across diverse pose variations. Restoring each frame independently in a naive manner inevitably introduces temporal incoherence and artifacts from pose changes and keypoint localization errors. To address this, we propose the first blind video face restoration approach with a novel parsing-guided temporal-coherent transformer (PGTFormer) without pre-alignment. PGTFormer leverages semantic parsing guidance to select optimal face priors for generating temporally coherent artifact-free results. Specifically, we pre-train a temporal-spatial vector quantized auto-encoder on high-quality video face datasets to extract expressive context-rich priors. Then, the temporal parse-guided codebook predictor (TPCP) restores faces in different poses based on face parsing context cues without performing face pre-alignment. This strategy reduces artifacts and mitigates jitter caused by cumulative errors from face pre-alignment. Finally, the temporal fidelity regulator (TFR) enhances fidelity through temporal feature interaction and improves video temporal consistency. Extensive experiments on face videos show that our method outperforms previous face restoration baselines. The code will be released on \href{https://github.com/kepengxu/PGTFormer}{https://github.com/kepengxu/PGTFormer}., Comment: 9 pages

In environmental health research, it is of interest to understand the effect of the neighborhood environment on health. Researchers have shown a protective association between green space around a person's residential address and depression outcomes. In measuring exposure to green space, distance buffers are often used. However, buffer distances differ across studies. Typically, the buffer distance is determined by researchers a priori. It is unclear how to identify an appropriate buffer distance for exposure assessment. To address geographic uncertainty problem for exposure assessment, we present a domain selection algorithm based on the penalized functional linear Cox regression model. The theoretical properties of our proposed method are studied and simulation studies are conducted to evaluate finite sample performances of our method. The proposed method is illustrated in a study of associations of green space exposure with depression and/or antidepressant use in the Nurses' Health Study., Comment: 27 pages, 5 figures

Estimating the 6D object pose from a single RGB image often involves noise and indeterminacy due to challenges such as occlusions and cluttered backgrounds. Meanwhile, diffusion models have shown appealing performance in generating high-quality images from random noise with high indeterminacy through step-by-step denoising. Inspired by their denoising capability, we propose a novel diffusion-based framework (6D-Diff) to handle the noise and indeterminacy in object pose estimation for better performance. In our framework, to establish accurate 2D-3D correspondence, we formulate 2D keypoints detection as a reverse diffusion (denoising) process. To facilitate such a denoising process, we design a Mixture-of-Cauchy-based forward diffusion process and condition the reverse process on the object features. Extensive experiments on the LM-O and YCB-V datasets demonstrate the effectiveness of our framework., Comment: CVPR 2024 CAMERA-READY